**1. Introduction**

The ship maneuver-induced motion in the partially-filled tanks by liquid, sloshing poses a thoughtful danger to the controllability and stability of this phenomenon. The entropy generation minimization method is used for the design of fluid flow motion system [1] as well as thermal systems [2–4] in recent years. Although the method is applied to the thermodynamic optimization of many finite-size systems and finite-time processes [5], the application in isothermal fluid flow is rare [6]. For the specific case of sloshing, as such systems are used to damping the solid motion [7], the minimization of entropy could not be a true objective function for optimization. Even if a new engineering application has emerged in the future where the minimization of the entropy in sloshing fluid is the aim, the fluid cannot consider as a complete thermodynamic system. The fluid motion is caused by a solid structure consists of internal damping which causes entropy generation. The entropy generation in an isothermal wall container could be a measure of viscous dissipation which produces heat and could cause to danger in flammable liquids.

The analytical solution of a similar problem was presented by Ibrahim [8]. The liquid sloshing dynamics of a liquid in a vessel with horizontal excitation was presented Ibrahim [8] while the entropy generation was not discussed. Ikegawa studied the fluid flow problem motion of a rigid container excited by a horizontal harmonic acceleration with Finite Element Methods [9]. His results used in many texts as a benchmark [1]. Damping of surface waves in an incompressible liquid is studied by Case and Parkinson [10].

Jamalabadi et al. [11] found the optimal design of circular baffles in the sloshing problem occurred in a rectangular tank which is horizontally coupled by a one-story structure. Their method was pure numeric, and the optimization was based on the vibration suppression of the liquid motion. Although the problem is a classic case [12–25], the study of its exergy is discussed comprehensively in rare studies [1,26]. The entropy analysis of the flow systems is performed in many flow motions [27–34], as well and the recent developments in fluid modeling [35–39].

The aim of the current paper is to derive an analytical expression for entropy generation isothermal sloshing phenomenon and discuss the use of entropy generation minimization for such systems. The analytical expression for entropy generation in the rectangular tanks is obtained for the first time in the rectangular storage tank.
